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The author is grateful to Peter B. Clark, David T. Coe, Alexander Hoffmaister, Fleming Larsen, Bennett T. McCallum, Enrique Mendoza, Steven A. Symansky and Michael A. Wattleworth for helpful comments and discussions. Any remaining errors are the author’s responsibility.
Fama (1976) introduces the concept of weak information sets which consist of current and past values of a random process. All variables are denoted in the current period, unless stated otherwise.
The model is consistent with linear rational expectations. However, it could also accommodate non-linear specifications by choosing a different g function.
Note that if the average forecast error is not zero, the projection is inefficient even if both β and ρ are zero.
Least squares regressions are used to estimate β and ρ.
This period was chosen because 1971 is the first year in which growth and inflation projections are available.
The pooled time series/cross section sample for the current year forecasts have 147 (= 7 x 21) observations, while the year ahead forecasts have 140.
For the pooled projections, the average forecast error is only 3 ½ percent of actual average output growth (0.1 of 1 percentage point compared with average growth of 2.7 percent) and about 2 ¾ percent of the actual average inflation (0.2 of 1 percentage point compared with average inflation of 7.1 percent).
The predicted variation is β2•σ2F, where σ2F is the variance of the forecast.
This implies, for example, that if ρ is significant the projection could be improved by adjusting for last period’s error.
The Theil inequality statistic is defined as the ratio of the root mean squared error of the World Economic Outlook forecast to the root mean squared error of the random walk forecast. If this ratio is less than one, it indicates that the World Economic Outlook forecast is better, that is, it has a lower average error than the random walk forecast. The random walk forecast for next period is the current period’s realization. These statistics are provided for comparison with Artis (1988).
Since growth and inflation are likely to be stationary, that is, tend to revert to a fixed mean, it is not difficult for a judgmental projection to outperform a random walk which does not have this property.
Unit roots tests were performed using the augmented Dickey-Fuller and the augmented Phillips-Perron for the 1950-91 period. The number of lags included in each of these tests was chosen following Campbell and Perron (1991).
Stationarity requires that θ1+θ2+…+θp<1, while invertibility requires that the roots of the characteristic equation α(L)=1-α1•L-α2•L2-…-αq•Lq = 0 must all lie outside the unit circle.
Under these, the lag length is selected by minimizing the functions (RSS+2•K•SEESQ)/T (Akaike) and (RSS+K•(logT)•SEESQ/T, where K and T are the number of regressors and observations, respectively, and RSS is the residual sum of squares and SEESQ is the standard error of the estimate squared.
Non-linear least squares estimations were performed using the Gauss-Newton algorithm with numerical partial derivatives and annual data. The data prior to 1971 were obtained from the Finance Statistics Tape of the International Monetary Fund. For Germany and Italy, data for 1950-55 were obtained from the OECD National Accounts.
Interestingly enough, the model for inflation not only describes essentially the same process across the seven countries, but the parameters estimates are also fairly close to each other.
Models estimated over the entire 1950-91 period were also consistent with these specifications.